Some curious points as to the relation of these systems may be noticed in Europe. It was observed of a certain deaf-and-dumb boy, Oliver Caswell, that he learnt to count as high as 50 on his fingers, but always ‘fived,’ reckoning, for instance, 18 objects as ‘both hands, one hand, three fingers.’[[333]] The suggestion has been made that the Greek use of πεμπάζειν, ‘to five,’ as an expression for counting, is a trace of rude old quinary numeration (compare Finnish lokket ‘to count,’ from lokke ‘ten’). Certainly, the Roman numerals I, II, ... V, VI ... X, XI ... XV, XVI, &c., form a remarkably well-defined written quinary system. Remains of vigesimal counting are still more instructive. Counting by twenties is a strongly marked Keltic characteristic. The cumbrous vigesimal notation could hardly be brought more strongly into view in any savage race than in such examples as Gaelic aon deug is da fhichead ‘one, ten, and two twenties,’ i.e., 51; or Welsh unarbymtheg ar ugain ‘one and fifteen over twenty,’ i.e., 36; or Breton unnek ha triugent ‘eleven and three twenties,’ i.e., 71. Now French, being a Romance language, has a regular system of Latin tens up to 100; cinquante, soixante, septante, huitante, nonante, which are to be found still in use in districts within the limits of the French language, as in Belgium. Nevertheless, the clumsy system of reckoning by twenties has broken out through the decimal system in France. The septante is to a great extent suppressed, soixante-quatorze, for instance, standing for 74; quatre-vingts has fairly established itself for 80, and its use continues into the nineties, quatre-vingt-treize for 93; in numbers above 100 we find six-vingts, sept-vingts, huit-vingts, for 120, 140, 160, and a certain hospital has its name of Les Quinze-vingts from its 300 inmates. It is, perhaps, the most reasonable explanation of this curious phenomenon, to suppose the earlier Keltic system of France to have held its ground, modelling the later French into its own ruder shape. In England, the Anglo-Saxon numeration is decimal, hund-seofontig, 70; hund-eahtatig, 80; hund-nigontig, 90; hund-teontig, 100; hund-enlufontig, 110; hund-twelftig, 120. It may be here also by Keltic survival that the vigesimal reckoning by the ‘score,’ threescore and ten, fourscore and thirteen, &c., gained a position in English which it has not yet totally lost.[[334]]
From some minor details in numeration, ethnological hints may be gained. Among rude tribes with scanty series of numerals, combination to make out new numbers is very soon resorted to. Among Australian tribes addition makes ‘two-one,’ ‘two-two,’ express 3 and 4; in Guachi ‘two-two’ is 4; in San Antonio ‘four and two-one’ is 7. The plan of making numerals by subtraction is known in North America, and is well shown in the Aino language of Yesso, where the words for 8 and 9 obviously mean ‘two from ten,’ ‘one from ten.’ Multiplication appears, as in San Antonio, ‘two-and-one-two,’ and in a Tupi dialect ‘two-three,’ to express 6. Division seems not known for such purposes among the lower races, and quite exceptional among the higher. Facts of this class show variety in the inventive devices of mankind, and independence in their formation of language. They are consistent at the same time with the general principles of hand-counting. The traces of what might be called binary, ternary, quaternary, senary reckoning, which turn on 2, 3, 4, 6, are mere varieties, leading up to, or lapsing into, quinary and decimal methods.
The contrast is a striking one between the educated European, with his easy use of his boundless numeral series, and the Tasmanian, who reckons 3, or anything beyond 2, as ‘many,’ and makes shift by his whole hand to reach the limit of ‘man,’ that is to say, 5. This contrast is due to arrest of development in the savage, whose mind remains in the childish state which the beginning of one of our nursery number-rhymes illustrates curiously. It runs—
‘One’s none,
Two’s some,
Three’s a many,
Four’s a penny,
Five’s a little hundred.’
To notice this state of things among savages and children raises interesting points as to the early history of grammar. W. von Humboldt suggested the analogy between the savage notion of 3 as ‘many’ and the grammatical use of 3 to form a kind of superlative, in forms of which ‘trismegistus,’ ‘ter felix,’ ‘thrice blest,’ are familiar instances. The relation of single, dual, and plural is well shown pictorially in the Egyptian hieroglyphics, where the picture of an object, a horse for instance, is marked by a single line | if but one is meant, by two lines | | if two are meant, by three lines | | | if three or an indefinite plural number are meant. The scheme of grammatical number in some of the most ancient and important languages of the world is laid down on the same savage principle. Egyptian, Arabic, Hebrew, Sanskrit, Greek, Gothic, are examples of languages using singular, dual, and plural number; but the tendency of higher intellectual culture has been to discard the plan as inconvenient and unprofitable, and only to distinguish singular and plural. No doubt the dual held its place by inheritance from an early period of culture, and Dr. D. Wilson seems justified in his opinion that it ‘preserves to us the memorial of that stage of thought when all beyond two was an idea of indefinite number.’[[335]]
When two races at different levels of culture come into contact, the ruder people adopt new art and knowledge, but at the same time their own special culture usually comes to a standstill, and even falls off. It is thus with the art of counting. We may be able to prove that the lower race had actually been making great and independent progress in it, but when the higher race comes with a convenient and unlimited means of not only naming all imaginable numbers, but of writing them down and reckoning with them by means of a few simple figures, what likelihood is there that the barbarian’s clumsy methods should be farther worked out? As to the ways in which the numerals of the superior race are grafted on the language of the inferior, Captain Grant describes the native slaves of Equatorial Africa occupying their lounging hours in learning the numerals of their Arab masters.[[336]] Father Dobrizhoffer’s account of the arithmetical relations between the native Brazilians and the Jesuits is a good description of the intellectual contact between savages and missionaries. The Guaranis, it appears, counted up to 4 with their native numerals, and when they got beyond, they would say ‘innumerable.’ ‘But as counting is both of manifold use in common life, and in the confessional absolutely indispensable in making a complete confession, the Indians were daily taught at the public catechising in the church to count in Spanish. On Sundays the whole people used to count with a loud voice in Spanish, from 1 to 1,000.’ The missionary, it is true, did not find the natives use the numbers thus learnt very accurately—‘We were washing at a blackamoor,’ he says.[[337]] If, however, we examine the modern vocabularies of savage or low barbarian tribes, they will be found to afford interesting evidence how really effective the influence of higher on lower civilization has been in this matter. So far as the ruder system is complete and moderately convenient, it may stand, but where it ceases or grows cumbrous, and sometimes at a lower limit than this, we can see the cleverer foreigner taking it into his own hands, supplementing or supplanting the scanty numerals of the lower race by his own. The higher race, though advanced enough to act thus on the lower, need not be itself at an extremely high level. Markham observes that the Jivaras of the Marañon, with native numerals up to 5, adopt for higher numbers those of the Quichua, the language of the Peruvian Incas.[[338]] The cases of the indigenes of India are instructive. The Khonds reckon 1 and 2 in native words, and then take to borrowed Hindi numerals. The Oraon tribes, while belonging to a race of the Dravidian stock, and having had a series of native numerals accordingly, appear to have given up their use beyond 4, or sometimes even 2, and adopted Hindi numerals in their place.[[339]] The South American Conibos were observed to count 1 and 2 with their own words, and then to borrow Spanish numerals, much as a Brazilian dialect of the Tupi family is noticed in the last century as having lost the native 5, and settled down into using the old native numerals up to 3, and then continuing in Portuguese.[[340]] In Melanesia, the Annatom language can only count in its own numerals to 5, and then borrows English siks, seven, eet, nain, &c. In some Polynesian islands, though the native numerals are extensive enough, the confusion arising from reckoning by pairs and fours as well as units, has induced the natives to escape from perplexity by adopting huneri and tausani.[[341]] And though the Esquimaux counting by hands, feet, and whole men, is capable of expressing high numbers, it becomes practically clumsy even when it gets among the scores, and the Greenlander has done well to adopt untrîte and tusinte from his Danish teachers. Similarity of numerals in two languages is a point to which philologists attach great and deserved importance in the question whether they are to be considered as sprung from a common stock. But it is clear that so far as one race may have borrowed numerals from another, this evidence breaks down. The fact that this borrowing extends as low as 3, and may even go still lower for all we know, is a reason for using the argument from connected numerals cautiously, as tending rather to prove intercourse than kinship.